Chaos in a simply formulated dry-friction oscillator

Chaotic oscillators with Coulomb-type friction were extensively studied in the past. However, these investigations mostly deal with rather complex mechanical models that are closely related to everyday’s engineering applications. In the present paper, we introduce a stick-slip oscillator consisting only of a spring and a block sliding on a rough surface, and the block is periodically forced. A simple friction law is implemented in which we consider sticking and sliding coefficients of friction. We show with the help of numerical simulation that the system can behave chaotically in certain parameter domains. We use common numerical techniques to visualize chaos and also try to estimate the value of the maximal Lyapunov exponent. We also point out the possibility of transient chaos by means of cobweb diagrams.